Turning Surface Finish Calculator: Feed & Nose Radius
Published September 22, 2026 · MfgWorkbench editorial reference
Estimate the geometric feed marks left by an ideal circular tool nose. This is a planning comparison for conventional round-nose geometry, not a measured surface roughness result.
Target Ra and inspection record — worked checks and practical limits.
Calculate and check
Default values are examples. Replace them with verified inputs for your job. Changing a unit or mode does not convert existing inputs.
Ra estimate versus peak-to-valley geometry
With feed f and nose radius r in mm, the common small-feed approximation is Ra ≈ f²/(32r), also in mm. Multiplying by 1000 gives micrometers. The exact circular cusp height in this model is h = r − √(r² − f²/4). The calculator reports that height separately; it is not a measured Rz value.
The Ra approximation is most useful when feed is small relative to nose radius. The software rejects f ≥ 2r, where this circular-intersection model breaks down. A wiper insert or a straight finishing land requires different geometry.
Example: feed has a squared effect
At f = 0.20 mm/rev and r = 0.8 mm, approximate Ra is 1.5625 µm and circular cusp height is 6.2746 µm. Halving feed to 0.10 mm/rev reduces the Ra estimate to 0.390625 µm—one quarter of the original. Doubling nose radius also lowers the ideal estimate, but only by a factor of two.
For an arithmetic target of Ra = 0.8 µm and r = 0.8 mm, rearranging the approximation gives f ≈ √(32 × 0.8 × 0.0008) = 0.1431 mm/rev. That is a model comparison, not a promise that the process will meet the drawing.
Why real surfaces differ
Built-up edge, runout, chatter, flank wear, material tearing and an inadequate minimum chip thickness can dominate the final profile. A larger nose radius can increase radial force and worsen vibration on a flexible part. Lowering feed indefinitely can create rubbing instead of a better surface.
Inspect with the parameter, filter, evaluation length and measurement direction specified on the drawing. Ra, Rq and Rz are not interchangeable, and there is no universal exact Ra-to-Rz conversion.
Reverse-check three theoretical Ra targets
For the same conventional circular nose radius of 0.8 mm, rearrange the approximation to f ≈ √(32 × r × Ra/1,000), with Ra entered in µm and the resulting feed in mm/rev. The division by 1,000 converts the roughness target to millimeters; omitting it makes the feed result about 31.6 times too large.
| Target Ra (µm) | Approximate equivalent (µin) | Calculated feed (mm/rev) |
|---|---|---|
| 0.4 | 15.75 | 0.10119 |
| 0.8 | 31.50 | 0.14311 |
| 1.6 | 62.99 | 0.20239 |
Doubling the target Ra allows only √2 times the feed in this model, not twice the feed. Enter 0.14311 mm/rev and 0.8 mm into the calculator: the approximate Ra should return about 0.80002 µm, with the small difference caused by rounding the feed. Keep the geometric peak-to-valley output separate; it is not a substitute for an Ra or Rz inspection.
Keep the prediction separate from the inspection record
| Model record | Actual inspection record |
|---|---|
| Feed; circular nose radius; approximate Ra; calculation revision | Measured parameter and result — not recorded |
| Assumptions: regular feed marks; no wiper geometry; no chatter model | Drawing requirement; instrument; filter/settings; evaluation length; measurement direction — not recorded |
| Candidate setup for a controlled trial | Part/feature; measurement locations; tool condition; acceptance decision — not recorded |
Fill the inspection column only after measuring a real surface using the specified method. If a trial misses the target, first distinguish geometry-related feed marks from vibration, built-up edge, wear or material tearing. Do not repeatedly lower feed below the tooling’s usable range simply because this ideal equation keeps predicting a lower number.
The table does not apply to wiper inserts or establish production capability. The basic approximation and its limitations are discussed in Predictive modeling of surface roughness and tool wear in hard turning using regression and neural networks. Review roughness parameters and unit conversions, and use the turning speeds-and-feeds calculator separately to check RPM and linear feed.
Content and numerical examples reviewed October 19, 2026. Examples are not production test results.
References and verification
Original explanations and worked examples by MfgWorkbench. Sources below support the stated concepts or selected reference data; they do not certify every example or a production application.
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Record the estimate separately from inspection
The second page of the free turning worksheet (PDF, 2 pages) compares approximate Ra with circular cusp height and provides separate fields for the drawing requirement, measurement setup and actual result. It does not treat theoretical geometry as a measured Rz. Browse the worksheet examples and limitations; download directly without an email address.